How does one animate time in the VSE?
In the VSE, the "multiply speed" value of a "Speed" effect strip can't be animated. You'll have to :


uncheck the "Stretch to input strip length" box,
check the "Use as speed" box,
set the "Speed Factor" value to 1 (so the video will be played at normal speed)
animate this value as you need:


greater than 1, playback will be faster,
between 0 and 1 the playback will be slower.



You may have to click the "Refresh Sequencer" button to see the result.

Note that the sound won't be affected by this effect strip. I don't know if you can time-remap a sound in Blender.